DIY: Diameter of Binary Tree

Problem statement

Given a binary tree, you need to compute the length of the tree’s diameter. The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.

Note: The length of the path between two nodes is represented by the number of edges between them.

Input

The input will be the root node of a binary tree. The following is an example input:

    1
   / \
  2   3
    /  \
   4    5
  /
 6

input = [1]

Output

The output will be an integer value representing the diameter. For the above input, the output will be:

4

The length of the path [2, 1, 3, 4, 6] is 4.

Coding exercise

Implement the diameter_of_binaryTree(root) function, where root is the root of the binary tree. The function returns an integer value representing the diameter of the tree.